UP整环上的u-有限表现型模  

u-finitely presented modules over UP-domains

作　　者：李庆[1] 杨军[1] 

机构地区：[1]西南民族大学计算机科学与技术学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2017年第6期618-622,共5页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金(11401493);四川省教育厅自然科学基金(14ZB0463);西南民族大学中央高校基本科研业务费专项资金(2015NZYQN69)

摘　　要：设R是UP整环.定义了u-有限型模和u-有限表现型模.证明了若M是u-有限型R-模,则有如下等价刻画:M是u-有限表现型模当且仅当存在u-正合列0→N→F→M→0,其中N是u-有限型R-模,F是有限生成投射R-模;当且仅当对任何u-正合列0→C→P→M→0,其中P是有限生成投射R-模,则C是u-有限型R-模;当且仅当存在u-正合列0→A→B→M→0,其中A是u-有限型R-模,B是u-有限表现型R-模.Let R be an UP-domain. u -finitely generated modules and u -finitely presented modules are defined. It is shown that if M is an u -finitely generated module, then M is an u -finitely presented module if and only if there exists an u -exact sequence 0 → N → F→ M→ 0 , where N is an u -finitely generated R -module and F is a finitely generated projective R -module; if and only if for each u -exact sequence 0 → C → P→M→ 0 , with P a finitely generated projective R -module, C is an u -finitely generated R-module ;if and only if there exists an u-exact sequence 0→ A→ B→ M→0 ,where A is an u-finitely generated R-module and B is an u -finitely presented R -module.

关 键 词：u-算子 UP整环 u-正合列 u-有限型模 u-有限表现型模 

分 类 号：O153.5[理学—数学]